Statistical inference of the stress-strength reliability for inverse Weibull distribution under an adaptive progressive type-Ⅱ censored sample

Xue Hu; Haiping Ren; Xue Hu; Haiping Ren

doi:10.3934/math.20231457

AIMS Mathematics

2023, Volume 8, Issue 12: 28465-28487. doi: 10.3934/math.20231457

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Research article

Statistical inference of the stress-strength reliability for inverse Weibull distribution under an adaptive progressive type-Ⅱ censored sample

Xue Hu ¹,
Haiping Ren ^{2
,
,}

1.
College of Science, Jiangxi University of Science and Technology, Ganzhou, 341000, China
2.
Teaching Department of Basic Subjects, Jiangxi University of Science and Technology, Nanchang, 330013, China

Received: 10 August 2023 Revised: 24 September 2023 Accepted: 11 October 2023 Published: 18 October 2023
MSC : 62F10, 62F15

In this paper, we investigate classical and Bayesian estimation of stress-strength reliability $\delta = P(X > Y)$ under an adaptive progressive type-Ⅱ censored sample. Assume that $X$ and $Y$ are independent random variables that follow inverse Weibull distribution with the same shape but different scale parameters. In classical estimation, the maximum likelihood estimator and asymptotic confidence interval are deduced. An approximate maximum likelihood estimator approach is used to obtain the explicit form. In Bayesian estimation, the Bayesian estimators are derived based on symmetric entropy loss function and LINEX loss function. Due to the complexity of integrals, we proposed Lindley's approximation to get the approximate Bayesian estimates. To compare the different estimators, we performed Monte Carlo simulations. Under gamma prior, the approximate maximum likelihood estimator performs better than Bayesian estimators. Under non-informative prior, the approximate maximum likelihood estimator has the same behavior as Bayesian estimators. In the end, two data sets are used to prove the effectiveness of the proposed methods.
- approximate maximum likelihood estimation,
- Bayesian estimation,
- inverse Weibull distribution,
- stress-strength reliability
Citation: Xue Hu, Haiping Ren. Statistical inference of the stress-strength reliability for inverse Weibull distribution under an adaptive progressive type-Ⅱ censored sample[J]. AIMS Mathematics, 2023, 8(12): 28465-28487. doi: 10.3934/math.20231457

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Abstract

In this paper, we investigate classical and Bayesian estimation of stress-strength reliability $\delta = P(X > Y)$ under an adaptive progressive type-Ⅱ censored sample. Assume that $X$ and $Y$ are independent random variables that follow inverse Weibull distribution with the same shape but different scale parameters. In classical estimation, the maximum likelihood estimator and asymptotic confidence interval are deduced. An approximate maximum likelihood estimator approach is used to obtain the explicit form. In Bayesian estimation, the Bayesian estimators are derived based on symmetric entropy loss function and LINEX loss function. Due to the complexity of integrals, we proposed Lindley's approximation to get the approximate Bayesian estimates. To compare the different estimators, we performed Monte Carlo simulations. Under gamma prior, the approximate maximum likelihood estimator performs better than Bayesian estimators. Under non-informative prior, the approximate maximum likelihood estimator has the same behavior as Bayesian estimators. In the end, two data sets are used to prove the effectiveness of the proposed methods.

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